I am not HMHW, but I wanted to respond to this. Humans follow physical law. Humans are part of nature. If you find litter in a forest, it is not supernatural, or even unnatural. Natural law can completely explain the presence of a plastic bag in the forest. Sentience (as blurrily defined as it is) exists in the observable universe, and fully conforms to natural laws.
This idea that things made by humans are unnatural is a pet peeve of mine and is especially untrue in this context where the opposite of “natural” is not “man-made”, but “supernatural”.
If god can interact in the universe in measurable ways then he is observable even if he can pick and choose when and how to do it. It just makes him difficult to observe, not impossible.
That’s just the case if we put an artificial cut-off on the ‘allowed’ complexity of natural laws – nobody’s claiming that the relatively simple descriptions we have now are anything close to the truth, so they might well be the extremely simplified limiting cases, and fundamental laws could in complexity approach and exceed human behaviour, in principle.
However, that’s not quite how I meant it, since human action is merely intermediate in some chain of causation; the action of a metaphysical entity on this universe would appear as ‘causeless’ events, taken as a given the assumption that the metaphysical is ‘hidden’ from science in some way. Thus, what we’d have would be things that happened apparently ‘on their own’, not through mediation by some agent that is part of this universe.
In principle, though, there are still greater problems in drawing up distinction between a physical and a metaphysical agent, provided the latter is supposed to act on the physical world, yet be non-observable; similarly, it could be said that ‘I’ act on the physical world, yet I’m not observable – everything you can observe is my interaction with photons, not me directly. It’s not any different with god, it seems to me.
It occurs to me I should clarify this a little – that human action is part of some chain of causation means that it can be broken down in such a way as to be describable by physical law; i.e. while you probably won’t find a singular, concise mathematical formula that describes the movement of a limb, all of its constituent parts follow established rules, down to the molecules and atoms. The internal rules are (reasonably well) known, and the external behaviours are just emergent ones from those rules. I believe this extends to the human mind, as well, down to brain structures, neural activity patterns, and eventually plain old electromagnetic interactions.
I would not presume similar for a metaphysical agent, since its inner workings are completely unknown, and of its outward actions, we can only observe the effects, which would appear in this universe as ‘first causes’. Those, then, would in effect form the underlying causative structure of this universe, and, if they indeed did follow rules, those rules would, no matter how complex, be fundamental physical laws (with randomness probably just being another rule, as well – there’s certainly no necessity for determinism in physics any more).
However, calling such an entity ‘god’ is at best some form of Spinozan pantheism, and at worst just given the laws of physics a different name.
Well, sure, I agree with all that; contrariwise though, I’m sure you’ll agree that there’s a bit of difference between “conforms to natural laws” and “describable by and indistinguishable from physical law” (emphasis mine).
I just felt that polarizing the positions to “describable by and indistinguishable from physical law” and “not intentionally acting” was excluding the middle, a middle which I feel happens to include the entire human race. As a member of the human race this bothers me a bit; surely there are better ways to disprove God than to disprove humans in the process.
It is a good point that a god’s interactions with the physical, being sourced outside of reality, would be percieved as first causes. I don’t feel that the relevent point isn’t that there would be natural laws to describe these actions, though (as human behavior isn’t described by natural laws, despite being limited by them) - the relevent point is that there are actually two ways for god to be: either so mindlessly consistent that his actions are perceived as natural laws, which would be inconsistent with the idea that he’s acting intentionally, or unpredictable and sporadic as we’d expect the behavior of a sentient being to be like, but in that case each action would appear as an inexplicable, physics-defying, radically unnatural ‘first cause’ action. And none of those have ever been observed, which haven’t later been found to be so mindlessly consistent as to merit a natural law being written.
Yes, I missed a term to guarantee correctness. The system must also be sound for that. Thanks for pointing it out.
(emphasis mine)
This is not a proper example of what you’re trying to show.
The field axioms are in no way a formal system.
They can’t even tell you about numbers. Or how the operators (+) and (•) work.
You can’t form the sentence ‘is there an x such that x • x = 2?’ from the field axioms, because the notion of ‘2’ doesn’t exist yet.
If you were trying to compare all the possible fields using numbers as we assume them, (natural, rational, real, etc) and the operations we normally expect from (+) and (•), it still isn’t a valid comparison:
It’s interesting to compare separate mathematical systems and see what they agree and disagree on. And it isn’t troubling to say that *two separate systems *have *different answers *to ‘is there an x such that x • x = 2?’. (Which is what you appear to be trying to say. And this is not the same as saying the question is undecidable when you consider both systems at once, because you did get an answer each time. So, your conglomerate system would be inconsistant, not undecidable.) But it would be troubling if the question can be perfectly well formed within one system, and you *can’t get *an answer.
So, although God is undecidable in ZFC, (not true because like 2 in a system with no numbers, you can’t even formulate the question,) someone can just propose a ZFC + God Hypothesis, and trivially decide it? And it’s no longer troubling? I wouldn’t propose to do it. And I’m troubled by trivially deciding the undecidible, because undecidible doesn’t mean there isn’t an answer, just that you can’t find it. So, if you capriciously decide it wrong, your system is no longer sound. And you would never know it.
And if so, ZFC +Axiom of Constructibility is an unsound system. And many new theorems depend on this. If it’s wrong, they are in doubt.
You OFTEN use a trivial example to disprove a logic statement. The trivial is often the easiest to show. It still disproves the statement. And it’s bad logic to say, “well, it was a trivial example, I’m still going to believe all the other implications of the statement.” The statement is invalidated. If it needed that trivial example in order to be true, all its implications are in doubt. Yes, you may be able to save some or all of them with a new statement, and that’s why mathematicians now go about proving that certain answers will exist, so that the theorems that depend on those answers existing are still sound.
edit:(just wanted to say I can’t stick around today. So, I’m not going to get to all the questions I would like to.)
I don’t understand what you mean by any of this. Here are the field axioms:
There are operators (+) and (*) and numbers 0 and 1 [and other numbers formable from those; e.g., 2 as 1 + 1, and so on].
For all numbers x, x + 0 = 0 + x = 1 * x = x * 1 = x.
For all numbers x and y, x + y = y + x and x * y = y * x.
For all numbers x, there exists a y such that x + y = 0.
For all numbers x, if x is not equal to 0, then there exists a y such that x * y = 1.
For all numbers x, y, and z, x * (y + z) = xy + xz.
These most definitely speak about the operators (+) and (•), and numbers such as 2. And why do you say the field axioms are in no way a formal system? We’ve left the term “formal system” unformalized so far, but what quality of such a thing are you saying the field axioms lack?
I still don’t understand what you think makes the field axioms different from any other axiom system, but let me point out that whenever the axioms T neither prove nor disprove A, it is because there are two different possible models of those axioms, one where T and A both hold, and one where T and NOT A both hold. This is not special to the field axioms; it is always the way. Your objection to independence results in the context of the field axioms would hold just as well for any independence results anywhere.
My point was that “undecidable”, in the context of Goedel’s results, only means “Neither provable nor disprovable from”. And this is never an absolute notion; it is always a relative notion. You can be undecidable from axiom system S but decidable from axiom system T. This is always the way. No particular statement is magically more intrinsically undecidable than another; it’s just with respect to particular axiom systems that we can say that some statements are undecidable.
I’m not claiming that Goedel’s proof is somehow wrong because it uses a trivial example; that would be silly. But my point is that, after carrying out a proof, you can come to realize that you were previously thinking of the just-established as being more profound than it actually is, which is exactly what was happening here.
As a similar example, suppose I were to tell you “An infinitesimal is a number so small that, no matter how many times you add it to itself, the result is never bigger in magnitude than 100.” You might say “Whoa, that’d have to be a pretty crazy number. Can you actually prove that such things exist?” And I’d say “Yeah, sure. 0 is infinitesimal, for example.” Your response at this point would probably be “Oh, heh. I guess it’s not necessarily so crazy a notion after all, since it covers such trivialities. Actually, now that I see your proof, I realize that the established result is actually kinda boring; I was thinking of it as more mind-blowing than it actually is.”.
(Anyway, my point with the field axioms was only to illustrate that discovering some particular axiom system to be incomplete is rarely surprising; most axiom systems are incomplete. Take your favorite non-redundant axiom system and remove an axiom; presto, you have something incomplete. The mere fact that some axiom systems are incomplete was recognized well before Goedel; that’s not the interesting thing about his result.)
I think we may have a different perspective on this. Everything humans do follow the laws of physics. Every decisions, emotion, and action is caused by chemical or electrical interactions that are theoretically just as predictable as the ones that take place in a test tube, a computer, or a sun. Our brains are high band width, self programming electro-chemical computers, and theoretically we could model them and predict how humans will react just as we can predict how molecules react.
As far as I could tell the question was a matter of categorization by obervable behavior. Human behavior is indeed the result of complex biological mechanics obeying physical law, but the resulting behavior itself cannot be reasonably described as “indistinguishable from physical law”. For one thing, physical law is a sight more consistent than people are, because people have internal state that varies based on internal processes that may or may not be visible from the outside.
From the ‘inside’ perspective, we’re millions(billions?) of component parts working together, each consistently obeying natural law. From the perspective of externally observing behavior, we’re hardly paragons of consistency.
Well, neither is the weather, yet it can still be mathematically predicted to some degree of accuracy; I don’t see why similar shouldn’t apply to humans. If all the parts follow rules, surely the whole does, too, even if those rules may be stupendously complicated and non-linear to such a degree that makes prediction nigh impossible.
Think of AI – do you think that’s possible? – it’s a set of rules that model human behaviour. Or a simulation of the whole world (let’s say it’s a perfect one, completely indistinguishable from the real world), which contains rules for each individual’s actions. If you then were to remove the actual humans from the simulation, yet leave the effects of their actions in it, you’d end up with a world in which a lot of things happen without apparent cause, yet still according to rules, namely those used to model human behaviour – these rules then would constitute natural laws in said virtual reality.
And we don’t describe the specific manifestations of weather behavior in terms of natural laws either. QED.
Of course AI is possible - all we’d have to do is scan somebody’s head and exactly simulate every minute particle and velocity. (This may take us a little while to actually pull off, of course.)
Whoops - that doesn’t give you a tidy short list of rules describing all of human behavior, does it? And even if you made such a list, it’s going to be totally dependent on a complicated internal state, complicated to a degree that we’re not going to be able to extrapolate what the rules are by observation.
Look. As far as I can tell, you are declaring that it’s a natural law that the pixel 110th over and 122nd down on your computer monitor is the precise color it is right now. That there are natural laws which can be referred to to look that up and calculate that. Me, I don’t believe for one hairy instant that we write natural laws at the macro scale like that, and you haven’t a snowball’s chance of convincing me we do. Not unless you can point me at the ten-billion page science book in which you can look up the screen-pixel-color law in.
We don’t – because there’s more fundamental levels than that. It’s very fortuitous that this is the case, but it’s not a logical necessity. Like in the case with the simulation sans humans, the macro level might be all we have. You’re saying that we can’t derive natural laws in that case, because they would be too complicated. Fine, I don’t particularly understand why you would take the rather bizarre stance that natural laws are only natural laws up to a certain level of complexity, but if you’re dead-set on doing so, knock yourself out. It’s just not a stance I share – the complicated fundamental rules are still fundamental rules, and natural law really isn’t anything else. Nobody guarantees us reality is easy.
The point is that you don’t have to go back to the micro-level to predict the weather. You wouldn’t start calculating the trajectories of all H[sub]2[/sub]O molecules in the atmosphere to determine whether or not it’s cloudy tomorrow. Instead, you can model the macroscopic behaviour of cloud fields. Now, if there were no microscopic structure – if there were only an entity called ‘cloud’, which behaved just like we observe clouds to, and no individual H[sub]2[/sub]O molecules – then the models for cloud behaviour in meteorology would be the most fundamental descriptions there are, regardless of whether or not you’d want to call them ‘natural laws’. Personally, I see no need to invent a new term for them, since I don’t see any kind of clear-cut distinction, but if you insist, I’m not gonna stop you.
We actually don’t have to creat a new word - you just supplied the existing one that works: “Model”. Human behavior can be described by models, which have the ability to account for internal state. It cannot be described by laws, which have this marked tendency to restrain themselves to a few dozen variables.
Regardless, if you feel so dedicated to the idea that all human behavior (in fact, all behavior of everything) should be lumped under the label “natural law”, then more power to you. I do think doing so confuses the discussion and robs the term of meaning, though.
Nah. I pretty explicitly only concerned myself with stuff not part of a causal chain within the natural world, i.e. the metaphysical. You brought in humans and the like. Human behaviour isn’t fundamental; the effects of actions of a metaphysical agent on this world would appear to be. Human actions can be broken down into, at the most fundamental level, elementary particles doing their thing. If I understand you correctly, it is those fundamental interactions that are to be described by ‘natural laws’. I’m certainly fine with that (even though I don’t really see why ‘higher-up’ descriptions, which would be contained, as emergent behaviours, within the more fundamental interactions, can’t be natural laws also); but, as I already said, metaphysical effects would appear just as fundamental, so I’m kinda at a loss why I’m not allowed to call those ‘natural laws’, too. But well, seeing how this is all just a really rather inconsequential terminological quibble, I’ll call them ‘models’ from now on (it’s certainly an applicable term – the mathematical descriptions of fundamental interactions being, in effect, simply models themselves).
Take it back a step. Would you say that radioactive decay follows natural laws? The fact that we cannot predict which atom in a lump of U-235 is going to decay does not change the fact that in about 700 million years half of it will have decayed.
You are confusing two things: Our ability to use natural laws to predict things and our ability to use natural laws to explain things. Any action you take can be explained using natural laws (given enough understanding of the processes in the human body). But it is possible that the interaction are so complex that they can never be truly predicted.
Things happen all the time that we can not current predict with complete accuracy. There are very few things that happen that we cannot explain, and I believe there is nothing that happens that we can not explain using natural law if we had sufficient data about the event.
Hmm, I think I see the terminological disconnect - fundamental interactions may be described by natural laws (or caused by them, depending how you’re using the term), but they’re not described as natural laws. So when you combine them into complex aggregate actions, the combined complex interactions are (obviously) no longer described by the individual laws that described their fundamental parts, and there is also clearly not caused by any single natural law that describes the aggregate action. So, the term no longer applies to them.
It’s kind of like how eggs are eggs and sugar is sugar and flour is flour and so forth, but when you make a cake out of it, the cake can no longer be described as being its component parts. The properties and definitions that apply to the aggregate’s parts don’t transfer up to the composite.
(Models can be used to describe and predict complex systems, which are similar to the way that human-written-equation-type natural laws can be used to predict the behavior of simple systems. Models of course are not analogous to the “natural laws cause and control basic interactions” defintion of the term ‘natural law’. So, they’re not completely analagous - and in the way you’re using the term here, they may not be analogous at all; I’m not sure.)
As for the supernatural, as I noted earlier, I agree fully that any supernatural interactions would appear to be first causes. I do think there’s a third possibility between “seeming like a mindless natural law, like that first cause we call ‘gravity’”, and “seeming like mindless randomity”, though, which is the reason why I argued that the dichotomy provided was an excluded middle. Clearly, if a sentient god existed, he could interact with the universe in the manner of a complex sentient being, which is unlikely to be mistaken for the simple constancy of a natural law, and which is also unlikely to be mistaken for pure randomity.
Of course, there is no evidence whatsoever that seemingly directed first causes are actually occuring.
Terminology be as it may, I don’t think I can agree with this. There’s no requirement that natural laws be simple. It’s nice if they turn out to be, but it could be that all laws so far known are just the extremely simplified limiting cases of a far more complex underlying description, every bit as complicated as the description of a sentient being. The only requirement is that the behaviour follows some sort of rules; if it doesn’t, I would think it to be random. A middle ground between the two would essentially amount to a libertarian free will – to actions that are both not determined by external circumstances, and yet subject to rational choice, which I think to be logically inconsistent. (In particular because, if an experimenter has free will, this implies that elementary particles also must have free will, via the free will theorem.)
Based on the definitions you are giving, the above argument is astoundingly dishonest. Based on your definitions there is no need for a “something inbetween”; every intentionally acting sentient entity, including all humans, functions quite nicely within the deceptively wide umbrella of “describable by and indistinguishable from physical law”. So, you are trying to trick the responder into thinking there is a problem that doesn’t exist.
It seems that the entire source of conflict was that I was assuming you were presenting an honest argument. Now that I have finally realized that that isn’t the case (okay, I’m slow), I can for the sake of argument accept your odd definitions, and withdraw.
Whoa there, that’s some pretty harsh words. What kind of problem was I trying to ‘trick’ you into thinking existed, and how does this make me dishonest? My stance, that I have been consistently and openly presenting during this little exchange, is as follows:
[ul][li]Things happen according to rules; then they’re describable, you can find models for them. (I’ll avoid the seemingly controversial term ‘natural laws’ here.)[/li][li]Things don’t happen according to rules; then they’re random, and not consistent with the assumption of intentional action.[/li][li]There’s some that say there’s a third possibility between the two, libertarian free will. I don’t think that’s a consistent proposition.[/ul][/li]
You’ll note that precisely this is present in both of the posts you quoted. You seemed to get ticked off by my usage of the term ‘natural laws’; alright, there’s always room to debate terminology. But if you’re actually intent on calling me dishonest because I was using the term in a way that you don’t agree with, then I think I’ll have to be done discussing with you.